Explanation Formula used: The arc length of the polar curve r = f ( θ ) on [ α , β ] is L = ∫ α β f ( θ ) 2 + f ′ ( θ ) 2 d θ . Given: The spiral is r = e − a θ and the interval is 0 ≤ θ ≤ π . Calculation: The derivative of the function r = e − a θ is evaluated as follows. f ′ ( θ ) = ( e − a θ ) ′ = − a e − a θ Thus, f ′ ( θ ) = − a e − a θ . Substitute f ( θ ) = e − a θ , f ′ ( θ ) = − a e − a θ , α = 0 and β = π in L = ∫ α β f ( θ ) 2 + f ′ ( θ ) 2 d θ as follows

Calculus: Early Transcendentals (3rd Edition)

3rd Edition

ISBN: 9780134763644

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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Chapter 12.3, Problem 79E

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To find: The length of the entire spiral r=e−aθ, for θ≥0 and a>0.

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Chapter 12.3, Problem 78E

Chapter 12.3, Problem 80E

Chapter 12 Solutions

Calculus: Early Transcendentals (3rd Edition)

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The length of the entire spiral r = e − a θ , for θ ≥ 0 and a > 0 .

Solution Summary: The author calculates the derivative of the function r=e-atheta .

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To find: The length of the entire spiral r=e−aθ, for θ≥0 and a>0.

Want to see the full answer?

Chapter 12 Solutions

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The length of the entire spiral r = e − a θ , for θ ≥ 0 and a &gt; 0 .

Solution Summary: The author calculates the derivative of the function r=e-atheta .

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To find: The length of the entire spiral r=e−aθ, for θ≥0 and a>0.

Want to see the full answer?

Chapter 12 Solutions

Additional Math Textbook Solutions

The length of the entire spiral r = e − a θ , for θ ≥ 0 and a > 0 .